Slashdot Mirror

← Back to Stories (view on slashdot.org)

42nd Mersenne Prime Confirmed

Posted by Zonk on from the wooo-party dept.

Jazzer_Techie writes "The possible Mersenne Prime discovered last week has now been confirmed. This prime has 7,816,230 digits, which makes it not only the largest Mersenne Prime, but also the largest prime of any kind ever discovered. For those who don't want to take time to read the article, the prime is 2^25,964,951 - 1."

26 of 296 comments (clear)

  1. 2^25,964,951 - 1 by Joey+Patterson · · Score: 5, Funny

    Can anyone post those digits in case the site gets /.'ed?

    1. Re:2^25,964,951 - 1 by mrspecialhead · · Score: 5, Funny

      Here's an Exclusive Binary Preview!

      11111111111111111111111111111111
      11111111111111111111111111111111
      11111111111111111111111111111111...

      --Your free demo has expired. For access to the rest of this content, please subscribe!--

    2. Re:2^25,964,951 - 1 by Eric+Smith · · Score: 5, Funny

      My web site has the full expansion in binary. It's over 25 megabytes, so please don't download it unless you really need it.

    3. Re:2^25,964,951 - 1 by TheSHAD0W · · Score: 5, Funny

      Hope your web server has gzip and/or bzip compression...

  2. Man. by DrEldarion · · Score: 5, Funny

    Those math freaks sure are a bunch of GIMPS.

  3. OMG by computerme · · Score: 4, Funny

    No Way!!

    2^25,964,951 - 1.

    Is my password! Oh Man, I guess everyone knows it now....

  4. And useful, too! by Eric+Smith · · Score: 4, Funny

    Now we can use the 41st and 42nd for a 50 megabit RSA key.

  5. Its the answer! by Rs_Conqueror · · Score: 5, Funny

    This is the 42nd one? I wonder if that means anything...

    --
    Behold, another webcomic!
  6. Participate in the search by Drooling_Sheep · · Score: 5, Informative

    GIMPS (Great Internet Mersenne Prime Search

    They have Windows, Linux, FreeBSD, and OS/2 clients.

  7. Why? by Ensign+Regis · · Score: 4, Insightful

    I'm not trying to be a troll here, but of what possible value is a really big prime number? Is there any practical value to it, or is it just an interesting bit of trivia?

    1. Re:Why? by irokitt · · Score: 4, Funny
      ...of what possible value is a really big prime number?


      I believe the search for Mersenne primes continues solely for the purpose of impressing women in bars. No, I don't think it would work either.
      --
      If my answers frighten you, stop asking scary questions.
    2. Re:Why? by MC68000 · · Score: 4, Informative

      The best reason for large Mersenne prime numbers that I can think of is that it gives data for mathematicians to formulate conjectures. There are many consequences to theoretical breakthroughs in the field of prime numbers, especially in the field of encryption, as the RSA algorithm requires large prime numbers.

      Note: This new prime number by itself is USELESS for encryption. There are only 42 Mersenne numbers, so they can't be used because there are insufficiently many.

      --
      E = m c^3 Don't drink and derive E = m c^3
    3. Re:Why? by MC68000 · · Score: 5, Interesting

      There actually are very good algorithms for finding primality. It has reached the point where proving a number prime is MUCH easier than finding any factors of it.

      There are two types. One is deterministic, and will give you absolute proof that the tested number is prime. The other type is probability based. These are more popular. The most widely used is known as the Miller-Rabin test. It is known to be absolutely correct for all n 3*10^16. For larger n, it will never report a composite to be prime, but there is a small (around 10^-20) chance the "prime" number will be composite. There are no known prime numbers that Miller-Rabin reports to be composite.

      In the case of Mersenne numbers, it's a different story. There is a deterministic algorithm called the Lucas-Lehmer test. This will determine whether 2^p-1 is prime with O-notation p! The catch of course is that it only works for Mersenne numbers.

      --
      E = m c^3 Don't drink and derive E = m c^3
    4. Re:Why? by onemorechip · · Score: 4, Funny

      It has reached the point where proving a number prime is MUCH easier than finding any factors of it.

      Unless the number in question is composite. In that case, it is MUCH easier to find factors of it, than to prove that it is a prime.

      --
      But, I wanted socialized health insurance!
  8. Might not be the 42nd largest by MarkByers · · Score: 4, Informative

    It is confirmed that it is a prime, but it hasn't yet been confirmed that it is the 42nd largest prime, because some numbers have not been checked.

    From TFA:

    However, note that the region between the 39th and 40th known Mersenne primes has not been completely searched, so it is not known if M20,996,011 is actually the 40th Mersenne prime.

    --
    I'll probably be modded down for this...
    1. Re:Might not be the 42nd largest by Eric+Smith · · Score: 4, Informative
      Of course it's not the 42nd largest prime. It's not even the 42nd largest known prime. It is the largest known prime.

      It is easily proven that there ISN'T a 42nd largest prime, because there isn't a largest prime.

  9. Mersenne GIMPS FAQ by bigtallmofo · · Score: 4, Insightful

    The FAQ for this endeavor can be seen here.

    One glaring ommission from the FAQ is "Why participate in this?" I guess if you have to ask why, there's no point in asking.

    --
    I'm a big tall mofo.
  10. PARENT NOT FLAMEBAIT (GIMPS:name of project) by Anonymous Coward · · Score: 4, Informative

    GIMPS is the name of the project that apparently was responsible for finding this, so the parent was a joke, not flame bait.

  11. "Not only" the largest Mersenne prime ... by gvc · · Score: 4, Informative

    The top three previously known primes were Mersenne. Here's a list. At the time they were discovered, almost all largest Mersenne primes have held the record for biggest prime until being edged out by another Mersenne prime. I am not sure when a non-Mersenne last had that status, but it is a rare occurrence.

    Looking for Mersennes is "picking the low fruit" when it comes to prime hunting so I question the phrasing "Not only is it the biggest Mersenne .."

    What would have been remarkable would have been if the new largest prime were *not* a Mersenne.

  12. Re:Largest known perfect number? by MC68000 · · Score: 5, Informative

    yes. There is a theorem due to Euclid that every even perfect number (a number which is the product of all of its divisors except itself) is of the form
    (2^n-1)*2^n. The given form does not apply to odd perfect numbers, but it is unknown whether any odd perfect numbers exist.

    --
    E = m c^3 Don't drink and derive E = m c^3
  13. Re:to put this into perspective by kanweg · · Score: 4, Funny


    So??

    Bill G.

  14. Big Deal - Javascript!! by XanC · · Score: 5, Funny

    I found it by leaving my browser open for a while on this page.

  15. Torrent by TorrentNinja · · Score: 4, Funny

    Here is a torrent of the prime number.. it's 25MB..

    M42.torrent

    Some good times testing bandwidth :)

  16. Re:Largest known perfect number? by CarlDenny · · Score: 4, Informative

    You mean a number which is the *sum* of all of its divisors except itself.

    A number which is the product of all its divisors except itself is, well, any product of exactly two primes.

  17. Re:Largest Prime? by MC68000 · · Score: 4, Informative

    That is not true. The number p1*p2*....*pn+1 is either a prime, OR it has a factor that is not one of the p's. In either case, you have a new prime, which as an aside proves that there are infinitely many primes.

    --
    E = m c^3 Don't drink and derive E = m c^3
  18. M42.gz.gz.base64 by Morosoph · · Score: 4, Interesting
    Homegrown, gziped twice, and base 64 encoded :-)
    begin-base64 644 M42.gz.gz
    H4sICOMCIUIAA000Mi5nei4A7dw9jgEBAAXgGbZ gI1Yi0SiMZDoamy00Cgqd
    RKMWvUPYKOmdgMQB9Jxis7XolEr i7woKId9XvfId4OWVJqnUNlFuBcnOz3ew
    3/wGV6NocdoVlp8 BAAAAAAAAAPDiRv/jZHgL0fmv3e0BAAAAAAAAAK9u8JX9
    uI8 Cjv1i89llAAAAAAAAAICHzRv1+LYFyB3Oq8rwmRcFvJF1nK+mM 7PaNLwA
    +SBAu5ViAAA=
    ====
    --
    Wikileaks, no DNS